The Indeterminacy of Philosophical Thinking

Some time ago, I wrote about the need to use plain language and clearly defined terms in a philosophical argument.  One of the things I noted was: When I hear an argument stated with "weasel-words" or phrasing that is semantically impenetrable, that is a glaring signal to me that I should be on the lookout for an attempt to evade cold, hard deductive reasoning.  Such is the case with a paper that has recently come to my attention by James Ross called Immaterial Aspects of Thought.  This argument hinges on the meaning of the word 'determinate' (or 'indeterminate').  But the word is not at all clearly defined.  Ross summarizes the argument this way:

Some thinking (judgment) is determinate in a way no physical process can be. Consequently, such thinking cannot be (wholly) a physical process.

This has been restated by Feser as a syllogism:

(1) All formal thinking is determinate, but
(2) No physical process is determinate, so
(3) No formal thinking is a physical process.

When I read these statements, the first thing that strikes me is that it isn't immediately obvious what they're saying.  There needs to be a clear and unequivocal definition of the word 'determinate', or this argument won't hold water.

Upon reading the paper by Ross, I could see that he seems to describe the term in two different ways.  One is as an imperfect approximation of the ideal Platonic or pure form (of a function).

Just as rectangular doors can approximate Euclidean rectangularity, so physical change can simulate pure functions but cannot realize them.

In this sense, formal thinking is determinate in that it is the perfect realization of the form, and a physical process is indeterminate in that it is an imperfect implementation of the form.  Taken this way, it means that a physical process would produce a result that is approximately correct, but inexact, just as a door is approximately a rectangle.  Let me label this definition as "formal indeterminacy". 

But Ross also describes indeterminacy in the sense of unpredictability of behavior.  That is, one can't say for sure which pure form is realized by the process.

There is nothing about a physical process, or any repetitions of it, to block it from being a case of incompossible forms ("functions"), if it could be a case of any pure form at all. That is because the differentiating point, the point where the behavioral outputs diverge to manifest different functions, can lie beyond the actual, even if the actual should be infinite; e.g., it could lie in what the thing would have done, had things been otherwise in certain ways. For instance, if the function is x(*)y = (x + y, if y < 10^40 years, = x + y + 1, otherwise), the differentiating output would lie beyond the conjectured life of the universe.

Let us ignore the incorrect mathematical notation and focus on what he's telling us: that we can't be certain what functional form is realized by the physical process.  This is an epistemological problem, and it is a completely different kind of indeterminacy.  In the first case, given that we know what the process does, we understand that it does it imperfectly.  In the second case, we can't be sure what it does.  Let me label this definition as "behavioral indeterminacy".

Another way to interpret what Ross is saying is that the process degrades, or doesn't perform as intended.  However, I think it is reasonable to limit the discussion to processes that perform normally.  If we want to include degraded performance, then it is only fair that we should also allow that the intellect can be degraded as well.  And then it is no longer reasonable to assert the first premise - that formal thinking is determinate.

So at this point, I have a problem.  I really don't know exactly what Ross is saying when the uses the word 'determinate'.  Perhaps Ed Feser can shed some light on it. 

In his article on this topic, Feser doesn't speak about what I have called formal indeterminacy - the inaccuracy or imperfection of the result.  Instead, he speaks of indeterminacy in yet another sense:

The physical properties are “indeterminate” in the sense that they don’t fix one particular meaning rather than another.  The same is true of any further symbol we might add to this one.  For example, suppose the sequence T-R-I-A-N-G-L-E appeared under Δ.  There is nothing in the physical properties of this sequence, any more than in Δ, that entails or fixes one particular meaning rather than another.  Its physical properties are perfectly compatible with its signifying triangles themselves, or the word “triangle,” or some weird guy who calls himself “Triangle,” or your favorite trip hop acid jazz, or any number of other things.

This is different from both senses in which Ross uses the term, because it focuses on the semantic interpretation of the function, not the physical implementation.  Let me label this definition as "semantic indeterminacy".  See my side note on this (*).

But that's not all.  Feser goes on to describe indeterminacy in a way that is consistent with what I have called behavioral indeterminacy in the Ross paper.

As Kripke points out, you might think that melting wires or slipping gears count as malfunctions, but relative to an eccentric program they might count as the machine doing exactly what it is supposed to be doing, whereas if the wires failed to melt or the gears failed to slip, that would be (relative to such a program) a malfunction.  Either way, the physical properties of the machine won’t tell you, no matter how long its operations continue or could continue.  Take the complete list of physical behaviors a given machine does exhibit or could exhibit -- a calculator’s outputs, the words and images on a computer screen, the noises a robot makes, or even a machine sputtering, melting, or emitting smoke and sparks.  There are always going to be alternative incompatible programs (even if eccentric ones like a program for computing Kripke’s “quus” function) that the machine’s behavior is consistent with.

This is the same epistemological problem that Ross described (even if Feser insists that it is not an epistemological problem).  The issue they describe is one of not knowing what function is implemented by the physical process.  See my second side note on this (**).

It is not my purpose in this article to refute Ross' Immaterial Aspects of Thought, but simply to point out what I see as a bad argument.  It's bad because of wording that is not clearly defined or understood.  In two different discussions, we have three distinct uses of the same term, and only one of them is common to both discussions.  Both of them use it in two distinctly different ways.  Ross' use of the term in the sense of formal indeterminacy appears nowhere in Feser's article, and Feser's use in the sense of semantic indeterminacy appears nowhere in Ross' paper.  Given this uncertainty in the definition of a word that is central to the argument, can they even be making the same argument?  Doubtful.  And this is what I call the indeterminacy of (bad) philosophical thinking.




(*) The notion of semantic indeterminacy in the context of this argument is self-defeating.  Formal thinking is generally expressed in symbolic terms.  For example, we define the function of squaring like this: n squared equals n times n.  This is symbolic.  According to Feser, it would be semantically indeterminate, because the n has no particular meaning attached to it.  But the first premise of the argument says that formal thinking is determinate.  That's a contradiction.  I think Feser's thinking is muddled in defining indeterminacy in this manner.

(**) Behavioral indeterminacy, as described by both Ross and Feser, is a problem of not knowing what function is implemented by a physical process.  But that would be true only in the case that the process is seen as a "black box", where we can observe only the inputs and outputs, but not the actual process itself.  If we can see the how the process works, this is no longer a problem.  For example, if we can examine the code running in a computer, any behavioral indeterminacy goes away.  We know exactly what it  does.  There is no possibility that the function will someday change to something different, unless that change is embedded in the code, in which case we know it, because be have examined the code.  So there is no behavioral indeterminacy if we can examine and understand the process itself.